What is the integral of 2xln(2x) ?

The integral of 2xln(2x) is x^2ln(2x)-(x^2)/2+C

Popular >

integral of 2xln(2x)

\int 2 x ln (2 x) d x

x^{2} ln (2 x) - \frac{x ^{2}}{2} + C

Solution steps

\int 2 x ln (2 x) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 2 \cdot \int x ln (2 x) d x

Apply Integration By Parts

: \frac{1}{2} x^{2} ln (2 x) - \int \frac{x}{2} d x

= 2 (\frac{1}{2} x^{2} ln (2 x) - \int \frac{x}{2} d x)

\int \frac{x}{2} d x = \frac{x ^{2}}{4}

= 2 (\frac{1}{2} x^{2} ln (2 x) - \frac{x ^{2}}{4})

Simplify

2 (\frac{1}{2} x^{2} ln (2 x) - \frac{x ^{2}}{4}) : x^{2} ln (2 x) - \frac{x ^{2}}{2}

= x^{2} ln (2 x) - \frac{x ^{2}}{2}

Add a constant to the solution

= x^{2} ln (2 x) - \frac{x ^{2}}{2} + C

y^{^{''}} - 6 y^{^{'}} + 10 y = 0

C (x) = \frac{4 x + 50}{x + 2}

\int x e^{11 x + 3} d x

\int (x + 3) (x^{2} + 1) d x

\int 4 arcsin (x) d x

What is the integral of 2xln(2x) ?
The integral of 2xln(2x) is x^2ln(2x)-(x^2)/2+C